Theory of photoluminescence of the nu=1 quantum Hall state: Excitons, spin waves, and spin textures

We study the theory of intrinsic photoluminescence of two-dimensional electron systems in the vicinity of the v=1 quantum Hall state. We focus predominantly on the recombination of a band of initial ''excitonic states'' that are the low-lying energy states of our model at v=1. It is shown that the recombination of excitonic states can account for recent observations of the polarization-resolved spectra of a high-mobility GaAs quantum well. The asymmetric broadening of the spectral line in the sigma_ polarization is explained to be the result of the ''shakeup'' of spin waves upon radiative recombination of excitonic states. We derive line shapes for the recombination of excitonic states in the presence of long-range disorder that compare favorably with the experimental observations. We also discuss the stabilities and recombination spectra of other (''charged'') initial states of our model. An additional high-energy line observed in experiment is shown to be consistent with the recombination of a positively charged state. The recombination spectrum of a negatively charged initial state, predicted by our model but not observed in the present experiments, is shown to provide a direct measure of the formation energy of the smallest ''charged spin texture'' of the v=1 state.